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Research Papers

# Analysis of Turbulent Scalar Flux Models for a Discrete Hole Film Cooling Flow

[+] Author and Article Information
Julia Ling

Mechanical Engineering Department,
Stanford University,
Stanford, CA 94305
e-mail: julial@stanford.edu

Kevin J. Ryan, John K. Eaton

Mechanical Engineering Department,
Stanford University,
Stanford, CA 94305

Julien Bodart

ISAE,
University of Toulouse,
Toulouse 31400, France

1J. Ling is currently at Sandia National Labs.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 20, 2015; final manuscript received September 8, 2015; published online October 21, 2015. Editor: Kenneth C. Hall.

J. Turbomach 138(1), 011006 (Oct 21, 2015) (7 pages) Paper No: TURBO-15-1182; doi: 10.1115/1.4031698 History: Received August 20, 2015; Revised September 08, 2015

## Abstract

Algebraic closures for the turbulent scalar fluxes were evaluated for a discrete hole film cooling geometry using the results from a high-fidelity large eddy simulation (LES). Several models for the turbulent scalar fluxes exist, including the widely used gradient diffusion hypothesis (GDH), the generalized GDH (GGDH), and the higher-order GDH (HOGGDH). By analyzing the results from the LES, it was possible to isolate the error due to these turbulent mixing models. Distributions of the turbulent diffusivity, turbulent viscosity, and turbulent Prandtl number were extracted from the LES results. It was shown that the turbulent Prandtl number varies significantly spatially, undermining the applicability of the Reynolds analogy for this flow. The LES velocity field and Reynolds stresses were fed into a Reynolds-averaged Navier–Stokes (RANS) solver to calculate the fluid temperature distribution. This analysis revealed in which regions of the flow various modeling assumptions were invalid and what effect those assumptions had on the predicted temperature distribution.

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## Figures

Fig. 1

Schematic of flow configuration. (a) Flow configuration with contours of θ¯. Coolant plenum and injection hole shown. (b) Comparison of LES and experimental results in near-injection region. Color contours of θ shown on the channel center-plane, as measured by Coletti et al. Corresponding isocontour lines from LES shown in black. (c) RANS domain. Zoomed-in section of mesh shown in region near hole exit. Isosurface of θ¯ = 0.01 also shown for reference.

Fig. 2

Contours of νt,LES/(UbD), αt,LES/(UbD), and Prt,LES in streamwise slices spaced 4D apart. The contours of αt,LES/(UbD) and Prt,LES are blanked in regions where D|∇θ¯|<0.1. Isosurface of θ¯=0.01 shown for reference. (a) νt,LES/(UbD). (b) αt,LES/(UbD).

Fig. 3

Contours of ϕ, the angle between the turbulent scalar fluxes predicted using algebraic closures and the LES turbulent scalar fluxes. Units are in radians. The slices are spaced 4d apart, and are blanked in regions where θ¯<0.01 or D|∇θ¯|<0.1. Isosurface of θ¯=0.01 shown for reference. (a) GDH; (b) GGDH; and (c) HOGGDH.

Fig. 4

Contours of θ¯ in streamwise slices spaced 4d apart from LES and RANS. Isosurface of θ¯=0.01 shown for reference. (a) LES. (b) Case 1: GDH with αt = αt,LES. (c) Case 2: GDH with Prt = 0.85. (d) Case 3: GDH with Prt = 0.6$. (e) Case 4: HOGGDH with CHODDGH = 0.6$. (f) Case 5: HOGGDH with CHODDGH = 1.5.

Fig. 5

Contours of η on the bottom wall. The region depicted extends 30D downstream of injection, and 2D on either side of the centerline. (a) LES. (b) Case 1: GDH with αt = αt,LES. (c) Case 2: GDH with Prt = 0.85. (d) Case 3: GDH with Prt = 0.6. (e) Case 4: HOGGDH with CHOGGDH = 0.6. (f) Case 5: HOGGDH with CHOGGDH = 1.5.

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